{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e2dd1d8a",
   "metadata": {},
   "source": [
    "例：柯西分布的分布函数为：$F(x)=\\frac{1}{\\pi}\\left(\\arctan x+\\frac{\\pi}{2}\\right),-\\infty<x<\\infty$，求柯西分布的密度函数？\n",
    "解：\n",
    "$$\n",
    "F^{'}(x) = p(x)=\\frac{1}{\\pi} \\frac{1}{1+x^{2}}, \\quad-\\infty<x<\\infty \n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d0cf89db",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\operatorname{atan}{\\left(x \\right)}}{\\pi} + \\frac{1}{2}$"
      ],
      "text/plain": [
       "atan(x)/pi + 1/2"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1.## 已知柯西分布的密度函数求分布函数\n",
    "from sympy import *\n",
    "x = symbols('x')\n",
    "p_x = 1/pi*(1/(1+x**2))\n",
    "integrate(p_x, (x, -oo, x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4d36dcff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{1}{\\pi \\left(x^{2} + 1\\right)}$"
      ],
      "text/plain": [
       "1/(pi*(x**2 + 1))"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2.## 已知柯西分布的分布函数求密度函数\n",
    "from sympy import *\n",
    "x = symbols('x')\n",
    "f_x = 1/pi*(atan(x)+pi/2)\n",
    "diff(f_x,x,1)  #f_x是要求导的函数，x是要对其求导的变量，n是可选的，表示求n阶导数，默认为1阶导数。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "f023a880",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "3.# 【0，1】上的均匀分布\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "a = float(0)\n",
    "b = float(1)\n",
    "\n",
    "x = np.linspace(a, b)\n",
    "y = np.full(shape = len(x),fill_value=1/(b - a))  # np.full 构造一个数组，用指定值填充其元素\n",
    "\n",
    "plt.plot(x,y,\"b\",linewidth=2)\n",
    "plt.ylim(0,1.2)\n",
    "plt.xlim(-1,2)\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('p (x)')\n",
    "plt.title('uniform distribution')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1436ae7",
   "metadata": {},
   "source": [
    "指数分布：\n",
    "\n",
    "若随机变量 $X$ 的密度函数为\n",
    "$$\n",
    "p(x)=\\left\\{\\begin{aligned}\n",
    "\\lambda e^{-\\lambda x}, & x \\geqslant 0 \\\\\n",
    "0, & x<0\n",
    "\\end{aligned}\\right.\n",
    "$$\n",
    "则称 $X$ 服从指数分布, 记作 $X \\sim \\operatorname{Exp}(\\lambda)$, 其中参数 $\\lambda>0$。其中 $\\lambda$ 是根据实际背景而定的正参数。假如某连续随机变量 $X \\sim \\operatorname{Exp}(\\lambda)$, 则表示 $X$ 仅可能取非负实数。\n",
    "\n",
    "指数分布的分布函数为：\n",
    "$$\n",
    "F(x)= \\begin{cases}1-\\mathrm{e}^{-\\lambda x}, & x \\geqslant 0 \\\\ 0, & x<0\\end{cases}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b1bd1936",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "4.# 指数分布\n",
    "lam = float(1.5)\n",
    "\n",
    "x = np.linspace(0,15,100)\n",
    "y = lam * np.e**(-lam * x)\n",
    "\n",
    "plt.plot(x,y,\"b\",linewidth=2) \n",
    "plt.xlim(-5,10)\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('p (x)')\n",
    "plt.title('exponential distribution')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97cb321b",
   "metadata": {},
   "source": [
    "正态分布（高斯分布）\n",
    "\n",
    "正态分布是《概率论与数理统计》中最重要的一个分布，高斯 (Gauss, 1777-1855)在 研究误差理论时首先用正态分布来刻画误差的分布，所以正态分布又称为高斯分布。\n",
    "\n",
    "若随机变量 $X$ 的密度函数为\n",
    "$$\n",
    "p(x)=\\frac{1}{\\sqrt{2 \\pi} \\sigma} \\mathrm{e}^{-\\frac{(x-\\mu)^{2}}{2 \\sigma^{2}}}, \\quad-\\infty<x<\\infty,\n",
    "$$\n",
    "则称 $X$ 服从正态分布， 称 $X$ 为正态变量， 记作 $X \\sim N\\left(\\mu, \\sigma^{2}\\right)$。 其中参数 $-\\infty<\\mu<\\infty, \\sigma>0$。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "9c1e2e38",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\sqrt{2} e^{- \\frac{\\mu^{2}}{2 \\sigma^{2}}} \\int\\limits_{-\\infty}^{x} e^{- \\frac{x^{2}}{2 \\sigma^{2}}} e^{\\frac{\\mu x}{\\sigma^{2}}}\\, dx}{2 \\sqrt{\\pi} \\sigma}$"
      ],
      "text/plain": [
       "sqrt(2)*exp(-mu**2/(2*sigma**2))*Integral(exp(-x**2/(2*sigma**2))*exp(mu*x/sigma**2), (x, -oo, x))/(2*sqrt(pi)*sigma)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "5.1## 已知正态分布的密度函数求分布函数\n",
    "from sympy import *\n",
    "from sympy.abc import mu,sigma\n",
    "x = symbols('x')\n",
    "p_x = 1/(sqrt(2*pi)*sigma)*E**(-(x-mu)**2/(2*sigma**2))\n",
    "integrate(p_x, (x, -oo, x))  #这个不能化简吗\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "02e0e3e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "5.2#正态分布\n",
    "import math\n",
    "mu = float(0)\n",
    "mu1 = float(2)\n",
    "sigma1 = float(1)\n",
    "sigma2 = float(1.25)*float(1.25)\n",
    "sigma3 = float(0.25)\n",
    "x = np.linspace(-5, 5, 1000)\n",
    "y1 = np.exp(-(x - mu)**2 / (2 * sigma1**2)) / (math.sqrt(2 * math.pi) * sigma1)\n",
    "y2 = np.exp(-(x - mu)**2 / (2 * sigma2**2)) / (math.sqrt(2 * math.pi) * sigma2)\n",
    "y3 = np.exp(-(x - mu)**2 / (2 * sigma3**2)) / (math.sqrt(2 * math.pi) * sigma3)\n",
    "y4 = np.exp(-(x - mu1)**2 / (2 * sigma1**2)) / (math.sqrt(2 * math.pi) * sigma1)\n",
    "plt.plot(x,y1,\"b\",linewidth=2,label=r'$\\mu=0,\\sigma=1$') \n",
    "plt.plot(x,y2,\"orange\",linewidth=2,label=r'$\\mu=0,\\sigma=1.25$') \n",
    "plt.plot(x,y3,\"yellow\",linewidth=2,label=r'$\\mu=0,\\sigma=0.5$') \n",
    "plt.plot(x,y4,\"b\",linewidth=2,label=r'$\\mu=2,\\sigma=1$',ls='--') \n",
    "plt.axvline(x=mu,ls='--')\n",
    "plt.text(x=0.05,y=0.5,s=r'$\\mu=0$')\n",
    "plt.axvline(x=mu1,ls='--')\n",
    "plt.text(x=2.05,y=0.5,s=r'$\\mu=2$')\n",
    "plt.xlim(-5,5)\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('p (x)')\n",
    "plt.title('normal distribution')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "63b7b8f9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "6.1# 使用scipy计算pdf画图(非自定义函数)\n",
    "from scipy.stats import expon # 指数分布\n",
    "x = np.linspace(0.01,10,1000)  \n",
    "plt.plot(x, expon.pdf(x),'r-', lw=5, alpha=0.6, label='expon pdf')    # pdf表示求密度函数值\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"p (x)\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "724dc1da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "6.2# 使用scipy计算cdf画图(非自定义函数)\n",
    "from scipy.stats import expon\n",
    "x = np.linspace(0.01,10,1000)  \n",
    "plt.plot(x, expon.cdf(x),'r-', lw=5, alpha=0.6, label='expon cdf')  # cdf表示求分布函数值\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"F (x)\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd337e2f",
   "metadata": {},
   "source": [
    "泊松分布：\n",
    "\n",
    "泊松分布是 1837 年由法国数学家泊松 (Poisson, 1781-1840)首次提出的，泊松分布的分布列为：\n",
    "$$\n",
    "P(X=x)=\\frac{\\lambda^{x}}{x !} e^{-\\lambda}\n",
    "$$\n",
    "其中： $\\lambda>0$ 是常数，是区间事件发生率的均值。泊松分布是一种常用的离散分布, 它常与单位时间 (或单位面积、单位产品等)上 的计数过程相联系, 譬如,\n",
    "   - 在一天内，来到某商场的顾客数。（$\\lambda$就是单位时间内商场的顾客数）\n",
    "   - 在单位时间内，一电路受到外界电磁波的冲击次数。\n",
    "   - 1 平方米内， 玻璃上的气泡数。\n",
    "   - 一铸件上的砂眼数。\n",
    "   - 在一定时期内， 某种放射性物质放射出来的 $\\alpha$-粒子数， 等等。 \n",
    "\n",
    "以上的例子都服从泊松分布。 因此泊松分布的应用面是十分广泛的。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "2a7a9d81",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEWCAYAAABrDZDcAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAYvklEQVR4nO3deZTV9Z3m8fcTCEeF4DIWHFkGMBIFg2AoMXZCSLemxW2YSceItiaxTQw9kI62M0r6nE5Om0zb7ehkQzEkIUbpSFrjjEAUxyXiElCqooJVNEJApCxaijFuqCHgZ/64l1gUVUVB1e9+L/V9XufUufyW+t2He8Tnfn+rIgIzM8vX+1IHMDOztFwEZmaZcxGYmWXORWBmljkXgZlZ5lwEZmaZcxGYmWXORWDZk7RGUpOkEwvY9mhJ70ha0Mk6R0n635K2S9ok6aKezmHWGReBGXwYeB74iwK2fROwsgvr7AAGA38JzC2ilMw64iKw7EXELuBxYHxPblfSdOBV4KFO1ulPqYD+PiLejIjHgUXAJT2ZxawzLgLLnqRDgenASR0sXyLp1Q5+lnTwOwOBa4Gr9vH2HwJ2RcTzreY9C3hEYBXTN3UAsyrwP4CXgCmSBkTEm60XRsS5B7DNbwI/jojNkjpbbwDwWpt5rwEfOID3NDsgLgLLmqTTgM9SGg38ltLxghXd3OYE4Azg5C6s/iYwsM28gcAb3clgtj9cBJYtSYcA84EZEfGKpGcpHSdY0Wa9+4DJHWzmsYg4q828TwIjgRfLo4EBQB9JYyPiI23WfR7oK2l0RKwrzxsPNBzY38ps/8m3obZcSboeODoi/qo8/R3g/RExs5vbPYw9v+X/N0rF8NcR0dLO+guBAL4ITADuBf4kIlwGVhE+WGxZkjQJOB+4stXsZ+iBM4ci4q2I+PfdP5R2/7yzuwQk3Sfp71r9yn8FDgW2AndQKgyXgFWMRwRmZpnziMDMLHOFFYGk+ZK2Snqug+WS9D1J6yWtktT2IJqZmVVAkSOCW4GpnSw/Cxhd/rkcmFtgFjMz60BhRRARjwKvdLLKNOC2KFkBHCHpmKLymJlZ+1JeRzAU2Nxquqk8b0vbFSVdTmnUQP/+/SeecMIJFQloxdvQsh2AY2v6J05i1rvV19dvi4ia9palLIL2rrtv9xSmiJgHzAOora2Nurq6InNZBV3wg+UA/PzLpyVOYta7SdrU0bKUZw01AcNbTQ8DmhNlMTPLVsoRwSJgVvmqylOB1yJir91C1rt95c9Gp45glr3CikDSHZTuuXK0pCbgG8D7ASLiFkqX0Z8NrAfeAi4tKotVr4+PPjp1BLPsFVYEEXHhPpYH0K17utjBr6G5dAfmE4ccnjiJWb58ZbElde3iRq5d3Jg6hlnWXARmZplzEZiZZc5FYGaWOReBmVnm/KhKS+rqqcenjmCWPReBJTVxxFGpI5hlz7uGLKn6Ta9Qv6mzm9SaWdFcBJbU9UvXcv3StaljmGXNRWBmljkXgZlZ5lwEZmaZcxGYmWXOp49aUl8/b2zqCGbZcxFYUr79tFl63jVkST2+bhuPr9uWOoZZ1jwisKS+//A6wE8qM0vJIwIzs8y5CMzMMuciMDPLnIvAzCxzPlhsSf3jp8eljmCWPReBJfXBmgGpI5hlz7uGLKkHG1/mwcaXU8cwy5pHBJbUDx/bAMAZYwcnTmKWL48IzMwy5yIwM8uci8DMLHMuAjOzzPlgsSX17QsmpI5glj0XgSU15IhDU0cwy16hu4YkTZW0VtJ6SbPbWX64pMWSnpXUIOnSIvNY9Vn8bDOLn21OHcMsa4UVgaQ+wE3AWcBY4EJJbZ9LOBNojIjxwCeBGyX1KyqTVZ8FKzaxYMWm1DHMslbkiGASsD4iNkTEDmAhMK3NOgF8QJKAAcArwM4CM5mZWRtFFsFQYHOr6abyvNbmAGOAZmA18NWIeLfthiRdLqlOUl1LS0tRec3MslRkEaidedFm+kzgGWAIMAGYI2ngXr8UMS8iaiOitqampqdzmpllrcgiaAKGt5oeRumbf2uXAndHyXpgI3BCgZnMzKyNIk8fXQmMljQKeAmYDlzUZp0XgdOBxyQNBo4HNhSYyarM3Isnpo5glr3CiiAidkqaBdwP9AHmR0SDpBnl5bcA3wRulbSa0q6kayJiW1GZrPoc1d8niZmlVugFZRFxL3Bvm3m3tPpzM/DnRWaw6nZnXel8gvNrh+9jTTMriu81ZEndVd/EXfVNqWOYZc1FYGaWOReBmVnmXARmZplzEZiZZc63obakbr10UuoIZtlzEVhSh/brkzqCWfa8a8iSun35C9y+/IXUMcyy5iKwpJas2sKSVVtSxzDLmovAzCxzLgIzs8y5CMzMMuciMDPLnE8ftaR+/uXTUkcwy55HBGZmmXMRWFLzHv0t8x79beoYZllzEVhSD63ZykNrtqaOYZY1F4GZWeZcBGZmmXMRmJllzqePWlKHvN93HzVLzUVgSf30r/w8ArPUvGvIzCxzLgJL6nsPreN7D61LHcMsay4CS+qJ9dt4Yv221DHMsuYiMDPLnIvAzCxzLgIzs8z59FFL6sjD+qWOYJY9F4EldcslE1NHMMteobuGJE2VtFbSekmzO1jnk5KekdQgaVmReczMbG+FjQgk9QFuAj4FNAErJS2KiMZW6xwB3AxMjYgXJQ0qKo9Vp39e+m8AXDP1hMRJzPJV5K6hScD6iNgAIGkhMA1obLXORcDdEfEiQET4xvSZ+c2m36WOYJa9IncNDQU2t5puKs9r7UPAkZIekVQv6XPtbUjS5ZLqJNW1tLQUFNfMLE9FFoHamRdtpvsCE4FzgDOBv5f0ob1+KWJeRNRGRG1NTU3PJzUzy1iRu4aagOGtpocBze2ssy0itgPbJT0KjAeeLzCXmZm1UuSIYCUwWtIoSf2A6cCiNuvcA0yW1FfSYcCpwJoCM1mVOebwQzjm8ENSxzDLWmEjgojYKWkWcD/QB5gfEQ2SZpSX3xIRayQtBVYB7wI/iojnispk1ec7009OHcEse4pou9u+utXW1kZdXV3qGGZmBxVJ9RFR294y32vIkvqHxQ38w+KG1DHMsuZbTFhSjc2vp45glj2PCMzMMuciMDPLnIvAzCxzPkZgSR1b0z91BLPsuQgsqes+fVLqCGbZ864hM7PMuQgsqa/dvYqv3b0qdQyzrHnXkCW1oWV76ghm2fOIwMwscy4CM7PMuQjMzDLnYwSW1NghA1NHMMtel4pA0pHAEOBt4IWIeLfQVJaNb5x3YuoIZtnrsAgkHQ7MBC4E+gEtwCHAYEkrgJsj4lcVSWlmZoXpbERwF3AbMDkiXm29QNJE4BJJx0bEjwvMZ73cFQufBvykMrOUOiyCiPhUJ8vqgfpCEllWtrz2TuoIZtnb51lDki5rM91H0jeKi2RmZpXUldNHT5d0r6RjJH0YWAF8oOBcZmZWIfs8aygiLpJ0AbAaeAu4MCKeKDyZmZlVxD6LQNJo4KvAL4AxlA4SPx0RbxUdznq/j4w4MnUEs+x15TqCxcDMiHhIkoC/BVYCPgHcuu2aqSekjmCWva4UwaSIeB0gIgK4UdKiYmOZmVmldHiwWNLHAXaXQGsRsU7SwPLBY7MDNuP2embc7jORzVLqbETwF5KuB5ZSumZg95XFxwF/CowArio8ofVqv3trR+oIZtnr7IKyK8v3GPoMcD5wDKV7Da0BfhARj1cmopmZFanTYwQR8Tvgh+UfMzPrhfw8AjOzzPl5BJbUx447OnUEs+y5CCypvzl9dOoIZtnryk3nDpH0t5LulvQLSVdKOqQrG5c0VdJaSeslze5kvVMk7ZL0mf0Jb2Zm3deVYwS3UbqK+PvAHEq3mbh9X78kqQ9wE3AWMBa4UNLYDtb7Z+D+rse23uLz85/i8/OfSh3DLGtd2TV0fESMbzX9K0nPduH3JgHrI2IDgKSFwDSgsc16X6F0H6NTurBN62Xe+cOu1BHMsteVEcHTkj66e0LSqUBX7j46FNjcarqpPO+PJA0F/gtwS2cbknS5pDpJdS0tLV14azMz66quFMGpwK8lvSDpBWA5MEXSakmrOvk9tTMv2kx/B7gmIjr9WhgR8yKiNiJqa2pquhDZzMy6qiu7hqYe4LabgOGtpocBzW3WqQUWlm5qytHA2ZJ2RsT/OcD3NDOz/dSVB9NsOsBtrwRGSxoFvARMBy5qs+1Ru/8s6VZgiUsgL6ePGZQ6gln2CruOICJ2SppF6WygPsD8iGiQNKO8vNPjApaHyz/xwdQRzLJX6AVlEXEvcG+bee0WQER8ocgsZmbWPt9ryJK64AfLueAHy1PHMMuai8DMLHMuAjOzzLkIzMwy5yIwM8ucb0NtSZ170jGpI5hlz0VgSV1y2sjUEcyy511DltTbO3bx9g7fgdQsJReBJfWFnzzFF37i5xGYpeQiMDPLnIvAzCxzLgIzs8y5CMzMMufTRy2pz0wcljqCWfZcBJbU+bXD972SmRXKu4YsqVe27+CV7TtSxzDLmkcEltRfL6gH4OdfPi1xErN8eURgZpY5F4GZWeZcBGZmmXMRmJllzgeLLamLPzoidQSz7LkILKnzxg9JHcEse941ZEk1v/o2za++nTqGWdY8IrCkrvz5M4CvIzBLySMCM7PMuQjMzDLnIjAzy5yLwMwscz5YbEl9afKxqSOYZa/QEYGkqZLWSlovaXY7y/9S0qryz68ljS8yj1WfM8YO5oyxg1PHMMtaYUUgqQ9wE3AWMBa4UNLYNqttBKZExEnAN4F5ReWx9yxbBuefD7W1pddly9LlOPeiN5nwiTeT5jDLXZEjgknA+ojYEBE7gIXAtNYrRMSvI+J35ckVgJ9bWLBly+Cqq2DrVhg8uPR61VWV/5/w7hzrDl/NjpNWJ8thZsUWwVBgc6vppvK8jlwG3NfeAkmXS6qTVNfS0tKDEfMzZw707w8DB8L73ld67d+/ND9Fjr59QUqXw8yKLQK1My/aXVH6U0pFcE17yyNiXkTURkRtTU1ND0bMz8aNMGDAnvMGDCjNzzGHmRVbBE1A6yeTDwOa264k6STgR8C0iPh/BeYxYNQoePPNPee9+WZpfo45zKzYIlgJjJY0SlI/YDqwqPUKkv4jcDdwSUQ8X2AWK5s1C7Zvh9dfh3ffLb1u316anyLHzp0QkS6HmRVYBBGxE5gF3A+sAf41IhokzZA0o7za14H/ANws6RlJdUXlsZIpU+DGG2HQIHj55dLrjTeW5qfIMWL7aPo+PzpZDjMDRbS7275q1dbWRl2d+8LMbH9Iqo+I2vaW+RYTllRD82s0NL+WNEO1XFdhloqLwJK6dnEj1y5uTPb+1XJdhVlKLoIK8jfP6lMt11WYpeQiqBB/86xOvp7BzEVQMf7mWZ18PYOZi6Bi/M2zOlXLdRVmKbkIKsTfPNt39dTjuXrq8cnev1quqzBLyUVQIf7m2b6JI45i4oij9pq/evVqRowYwdy5c7v9Hrt27eLkk0/m3HPPbXf5lClw2WVLeeON43n66eNYvvyfuv2eZgcTF0GF+Jtn++o3vUL9plf2mj9u3DgWLlzIbbfd1u33+O53v8uYMWM6XL5r1y5mzpzJfffdR2NjI3fccQeNjelOaTWrNBdBBU2ZAnfeCXV1pdfcSwDg+qVruX7p2naXDRo0iIaGhm5tv6mpiV/+8pd88Ytf7HCdp556iuOOO45jjz2Wfv36MX36dO65555uva/ZwcTPLLaqNXv2bH7/+9+zadMmRowYsceyyZMn88Ybb+z1OzfccANnnHHGH6evuOIKrr/++nbX3e2ll15i+PD3bpQ7bNgwnnzyyR74G+yfZctKZ5Ft3Fg6djRrlr8sWGW4CKwqLV26lO3bt3POOefQ0NCwVxE89thj+9zGkiVLGDRoEBMnTuSRRx7pcL327rcltfc4jeLsvs6kf/89rzPx7kOrBO8asqrzzjvvcPXVV3PzzTczbtw4nnvuub3WmTx5MhMmTNjr58EHH/zjOk888QSLFi1i5MiRTJ8+nYcffpiLL754r20NGzaMzZvfe5heU1MTQ4YMKeYv1wFfZ2IpeURgVedb3/oWn/vc5xg5ciTjxo1j0aJFe63TlRHBddddx3XXXQfAI488wg033MCCBQv2Wu+UU05h3bp1bNy4kaFDh7Jw4UJ+9rOfdf8vsh82biyNBFrzdSZWKR4RWFJfP28sXz9v7B+n165dywMPPMAVV1wB0OGIoLvOPvtsmptLD8zr27cvc+bM4cwzz2TMmDF89rOf5cQTT+zx9+yMrzOxlPw8ArMq0PoYwYABpRLYvt3HCKzn+HkEVrUeX7eNx9dtSx0jOV9nYillcYzAp+VVr+8/vA6Aj48+OnGS9KZM8X+XlkavHxH49s9mZp3r9UXg0/LMus4PT8pTry8C3/7ZrGs8es5Xry8Cn5Zn1jUePeer1x8snjWr9K0G9jwtL/fbP1eLf/z0uNQRrMwXteWr148IfFpedftgzQA+WDNg3yta4Tx6zlevHxGAT8urZg82vgzAGWMH72NNK5pHz/nq9SMCq24/fGwDP3xsQ+oYRnWNnn32UmVlMSIws66phtGzb8ldeR4RmFlV8dlLleciMLOqUk3X/uSyi8pFYGZVpVrOXsrpAjsXgSX17Qsm8O0LJqSOYVVk1qzS2Uqvvw7vvlt6TXH2UjXtoip6ZFJoEUiaKmmtpPWSZrezXJK+V16+StJHisxj1WfIEYcy5IhDU8ewKlItZy9Vyy6qSoxMCjtrSFIf4CbgU0ATsFLSoohobLXaWcDo8s+pwNzyq2Vi8bOlp4SdN76yzwi26lYNZy+NGlX6n+7Age/NS7GLqvXIBN57nTOn5z6jIkcEk4D1EbEhInYAC4FpbdaZBtwWJSuAIyQdU2AmqzILVmxiwYpNqWOY7aVadlFVYmRSZBEMBTa3mm4qz9vfdZB0uaQ6SXUtLS09HtTMrK1q2UVViYPnRV5QpnbmtX1AclfWISLmAfOg9Mzi7kczM9u3athFVYlbfxQ5ImgChreaHgY0H8A6ZmbZqsTIpMgRwUpgtKRRwEvAdOCiNussAmZJWkjpIPFrEbGlwExmZgedokcmhRVBROyUNAu4H+gDzI+IBkkzystvAe4FzgbWA28BlxaVx6rT3Isnpo5glr1CbzoXEfdS+p9963m3tPpzADOLzGDV7aj+/VJHMMueryy2pO6s28yddZv3vaKZFcZFYEndVd/EXfVNqWOYZc1FYGaWOReBmVnmXARmZplzEZiZZc7PLLakbr10UuoIZtlzEVhSh/brkzqCWfa8a8iSun35C9y+/IXUMcyy5iKwpJas2sKSVb69lFlKLgIzs8y5CMzMMuciMDPLnIvAzCxzKt0J+uAhqQU42J92fjSwLXWIKuLPY0/+PN7jz2JP3fk8RkRETXsLDroi6A0k1UVEbeoc1cKfx578ebzHn8Weivo8vGvIzCxzLgIzs8y5CNKYlzpAlfHnsSd/Hu/xZ7GnQj4PHyMwM8ucRwRmZplzEZiZZc5FUEGShkv6laQ1khokfTV1ptQk9ZH0tKQlqbOkJukISXdJ+rfyfyOnpc6UkqQry/9OnpN0h6RDUmeqJEnzJW2V9FyreUdJekDSuvLrkT3xXi6CytoJXBURY4CPAjMljU2cKbWvAmtSh6gS3wWWRsQJwHgy/lwkDQX+BqiNiA8DfYDpaVNV3K3A1DbzZgMPRcRo4KHydLe5CCooIrZExG/Kf36D0j/0oWlTpSNpGHAO8KPUWVKTNBD4BPBjgIjYERGvJg2VXl/gUEl9gcOA5sR5KioiHgVeaTN7GvDT8p9/CvznnngvF0EikkYCJwNPJo6S0neAq4F3E+eoBscCLcBPyrvKfiSpf+pQqUTES8ANwIvAFuC1iPi/aVNVhcERsQVKXyyBQT2xURdBApIGAL8AroiI11PnSUHSucDWiKhPnaVK9AU+AsyNiJOB7fTQsP9gVN73PQ0YBQwB+ku6OG2q3stFUGGS3k+pBP4lIu5OnSehjwH/SdILwELgzyQtSBspqSagKSJ2jxDvolQMuToD2BgRLRHxB+Bu4E8SZ6oGL0s6BqD8urUnNuoiqCBJorQPeE1E/K/UeVKKiK9FxLCIGEnpIODDEZHtN76I+Hdgs6Tjy7NOBxoTRkrtReCjkg4r/7s5nYwPnreyCPh8+c+fB+7piY327YmNWJd9DLgEWC3pmfK8v4uIe9NFsiryFeBfJPUDNgCXJs6TTEQ8Keku4DeUzrZ7msxuNyHpDuCTwNGSmoBvAP8E/KukyyiV5fk98l6+xYSZWd68a8jMLHMuAjOzzLkIzMwy5yIwM8uci8DMLHMuArNuKN9RdqOko8rTR5anR6TOZtZVLgKzboiIzcBcSud3U36dFxGb0qUy2z++jsCsm8q3DakH5gNfAk6OiB1pU5l1na8sNuumiPiDpP8OLAX+3CVgBxvvGjLrGWdRul3yh1MHMdtfLgKzbpI0AfgUpafOXbn77pBmBwsXgVk3lO+MOZfSsyVeBP4npQeqmB00XARm3fMl4MWIeKA8fTNwgqQpCTOZ7RefNWRmljmPCMzMMuciMDPLnIvAzCxzLgIzs8y5CMzMMuciMDPLnIvAzCxz/x8/4H+PVrSAgAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "6.3# 对比不同的lambda对泊松分布的影响\n",
    "import math\n",
    "# 构造泊松分布列的计算函数\n",
    "def poisson(lmd,x):\n",
    "    return pow(lmd,x)/math.factorial(x)*math.exp(-lmd)\n",
    "x = [i+1 for i in range(10)]\n",
    "lmd1 = 0.8\n",
    "lmd2 = 2.0\n",
    "lmd3 = 4.0\n",
    "lmd4 = 6.0\n",
    "p_lmd1 = [poisson(lmd1,i) for i in x]\n",
    "p_lmd2 = [poisson(lmd2,i) for i in x]\n",
    "p_lmd3 = [poisson(lmd3,i) for i in x]\n",
    "p_lmd4 = [poisson(lmd4,i) for i in x]\n",
    "\n",
    "plt.scatter(np.array(x), p_lmd1, c='b',alpha=0.7)\n",
    "plt.axvline(x=lmd1,ls='--')\n",
    "plt.text(x=lmd1+0.1,y=0.1,s=r\"$\\lambda=0.8$\")\n",
    "plt.ylim(-0.1,1)\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"p (x)\")\n",
    "plt.title(r\"$\\lambda = 0.8$\")\n",
    "plt.show()\n",
    "\n",
    "plt.scatter(np.array(x), p_lmd2, c='b',alpha=0.7)\n",
    "plt.axvline(x=lmd2,ls='--')\n",
    "plt.text(x=lmd2+0.1,y=0.1,s=r\"$\\lambda=2.0$\")\n",
    "plt.ylim(-0.1,1)\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"p (x)\")\n",
    "plt.title(r\"$\\lambda = 2.0$\")\n",
    "plt.show()\n",
    "\n",
    "plt.scatter(np.array(x), p_lmd3, c='b',alpha=0.7)\n",
    "plt.axvline(x=lmd3,ls='--')\n",
    "plt.text(x=lmd3+0.1,y=0.1,s=r\"$\\lambda=4.0$\")\n",
    "plt.ylim(-0.1,1)\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"p (x)\")\n",
    "plt.title(r\"$\\lambda = 4.0$\")\n",
    "plt.show()\n",
    "\n",
    "plt.scatter(np.array(x), p_lmd4, c='b',alpha=0.7)\n",
    "plt.axvline(x=lmd4,ls='--')\n",
    "plt.text(x=lmd4+0.1,y=0.1,s=r\"$\\lambda=6.0$\")\n",
    "plt.ylim(-0.1,1)\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"p (x)\")\n",
    "plt.title(r\"$\\lambda = 6.0$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "5af3d91a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0-1分布的数字特征：均值:0.5；方差:0.25；标准差:0.5\n",
      "二项分布b(100,0.5)的数字特征：均值:50.0；方差:25.0；标准差:5.0\n",
      "泊松分布P(0.6)的数字特征：均值:0.6；方差:0.6；标准差:0.7745966692414834\n",
      "特定离散随机变量的数字特征：均值:3.5；方差:2.916666666666666；标准差:1.707825127659933\n",
      "均匀分布U(1,1+5)的数字特征：均值:3.5；方差:2.083333333333333；标准差:1.4433756729740643\n",
      "正态分布N(0,0.0001)的数字特征：均值:0.0；方差:0.0001；标准差:0.01\n",
      "指数分布Exp(5)的数字特征：均值:0.2；方差:0.04000000000000001；标准差:0.2\n",
      "标准正态分布的数字特征：均值:-6.963277549967673e-16；方差:0.9999999993070242；标准差:0.999999999653512\n",
      "Exp(5.0)分布的数字特征：均值:0.20826187507584426；方差:0.03678414422845682；标准差:0.19179192951857182\n",
      "dist分布的数字特征：均值:3.333333333333333；方差:1.388888888888891；标准差:1.1785113019775801\n"
     ]
    }
   ],
   "source": [
    "7# 使用scipy计算常见分布的均值与方差：(如果忘记公式的话直接查，不需要查书了)\n",
    "from scipy.stats import bernoulli   # 0-1分布\n",
    "from scipy.stats import binom   # 二项分布\n",
    "from scipy.stats import poisson  # 泊松分布\n",
    "from scipy.stats import rv_discrete # 自定义离散随机变量\n",
    "from scipy.stats import uniform # 均匀分布\n",
    "from scipy.stats import expon # 指数分布\n",
    "from scipy.stats import norm # 正态分布\n",
    "from scipy.stats import rv_continuous  # 自定义连续随机变量\n",
    "\n",
    "print(\"0-1分布的数字特征：均值:{}；方差:{}；标准差:{}\".format(bernoulli(p=0.5).mean(), \n",
    "                                  bernoulli(p=0.5).var(), \n",
    "                                  bernoulli(p=0.5).std()))\n",
    "print(\"二项分布b(100,0.5)的数字特征：均值:{}；方差:{}；标准差:{}\".format(binom(n=100,p=0.5).mean(), \n",
    "                                  binom(n=100,p=0.5).var(), \n",
    "                                  binom(n=100,p=0.5).std()))\n",
    "## 模拟抛骰子的特定分布\n",
    "xk = np.arange(6)+1\n",
    "pk = np.array([1.0/6]*6)\n",
    "print(\"泊松分布P(0.6)的数字特征：均值:{}；方差:{}；标准差:{}\".format(poisson(0.6).mean(), \n",
    "                                  poisson(0.6).var(), \n",
    "                                  poisson(0.6).std()))\n",
    "print(\"特定离散随机变量的数字特征：均值:{}；方差:{}；标准差:{}\".format(rv_discrete(name='dice', values=(xk, pk)).mean(), \n",
    "                                  rv_discrete(name='dice', values=(xk, pk)).var(), \n",
    "                                  rv_discrete(name='dice', values=(xk, pk)).std()))\n",
    "print(\"均匀分布U(1,1+5)的数字特征：均值:{}；方差:{}；标准差:{}\".format(uniform(loc=1,scale=5).mean(), \n",
    "                                  uniform(loc=1,scale=5).var(), \n",
    "                                  uniform(loc=1,scale=5).std()))\n",
    "print(\"正态分布N(0,0.0001)的数字特征：均值:{}；方差:{}；标准差:{}\".format(norm(loc=0,scale=0.01).mean(), \n",
    "                                  norm(loc=0,scale=0.01).var(), \n",
    "                                  norm(loc=0,scale=0.01).std()))\n",
    "\n",
    "lmd = 5.0  # 指数分布的lambda = 5.0\n",
    "print(\"指数分布Exp(5)的数字特征：均值:{}；方差:{}；标准差:{}\".format(expon(scale=1.0/lmd).mean(), \n",
    "                                  expon(scale=1.0/lmd).var(), \n",
    "                                  expon(scale=1.0/lmd).std()))\n",
    "\n",
    "## 自定义标准正态分布\n",
    "class gaussian_gen(rv_continuous):\n",
    "    def _pdf(self, x): # tongguo \n",
    "        return np.exp(-x**2 / 2.) / np.sqrt(2.0 * np.pi)\n",
    "gaussian = gaussian_gen(name='gaussian')\n",
    "print(\"标准正态分布的数字特征：均值:{}；方差:{}；标准差:{}\".format(gaussian().mean(), \n",
    "                                  gaussian().var(), \n",
    "                                  gaussian().std()))\n",
    "\n",
    "## 自定义指数分布\n",
    "import math\n",
    "class Exp_gen(rv_continuous):\n",
    "    def _pdf(self, x,lmd):\n",
    "        y=0\n",
    "        if x>0:\n",
    "            y = lmd * math.e**(-lmd*x)\n",
    "        return y\n",
    "Exp = Exp_gen(name='Exp(5.0)')\n",
    "print(\"Exp(5.0)分布的数字特征：均值:{}；方差:{}；标准差:{}\".format(Exp(5.0).mean(), \n",
    "                                  Exp(5.0).var(), \n",
    "                                  Exp(5.0).std()))\n",
    "\n",
    "## 通过分布函数自定义分布\n",
    "class Distance_circle(rv_continuous):                 #自定义分布xdist\n",
    "    \"\"\"\n",
    "    向半径为r的圆内投掷一点，点到圆心距离的随机变量X的分布函数为:\n",
    "    if x<0: F(x) = 0;\n",
    "    if 0<=x<=r: F(x) = x^2 / r^2\n",
    "    if x>r: F(x)=1\n",
    "    \"\"\"\n",
    "    def _cdf(self, x, r):                   #累积分布函数定义随机变量\n",
    "        f=np.zeros(x.size)                  #函数值初始化为0\n",
    "        index=np.where((x>=0)&(x<=r))           #0<=x<=r\n",
    "        f[index]=((x[index])/r[index])**2       #0<=x<=r\n",
    "        index=np.where(x>r)                     #x>r\n",
    "        f[index]=1                              #x>r\n",
    "        return f\n",
    "dist = Distance_circle(name=\"distance_circle\")\n",
    "print(\"dist分布的数字特征：均值:{}；方差:{}；标准差:{}\".format(dist(5.0).mean(), \n",
    "                                  dist(5.0).var(), \n",
    "                                  dist(5.0).std()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "ae9afeef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "8.1# 绘制二维正态分布的联合概率密度曲面图\n",
    "from scipy.stats import multivariate_normal\n",
    "from mpl_toolkits.mplot3d import axes3d\n",
    "x, y = np.mgrid[-5:5:.01, -5:5:.01]  # 返回多维结构\n",
    "pos = np.dstack((x, y))\n",
    "rv = multivariate_normal([0.5, -0.2], [[2.0, 0.3], [0.3, 0.5]])\n",
    "z = rv.pdf(pos)\n",
    "plt.figure('Surface', facecolor='lightgray',figsize=(12,8))\n",
    "ax = plt.axes(projection='3d')\n",
    "ax.set_xlabel('X', fontsize=14)\n",
    "ax.set_ylabel('Y', fontsize=14)\n",
    "ax.set_zlabel('P (X,Y)', fontsize=14)\n",
    "ax.plot_surface(x, y, z, rstride=50, cstride=50, cmap='jet')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "5bca31e4",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/57/_0g_czzs1y90csygnbflyrv00000gn/T/ipykernel_30531/2813503570.py:11: UserWarning: The following kwargs were not used by contour: 'rstride', 'cstride'\n",
      "  ax2.contourf(x, y, z, rstride=50, cstride=50, cmap='jet')\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "8.2# 绘制二维正态分布的联合概率密度等高线图\n",
    "from scipy.stats import multivariate_normal\n",
    "x, y = np.mgrid[-1:1:.01, -1:1:.01]\n",
    "pos = np.dstack((x, y))\n",
    "rv = multivariate_normal([0.5, -0.2], [[2.0, 0.3], [0.3, 0.5]])\n",
    "z = rv.pdf(pos)\n",
    "fig = plt.figure(figsize=(8,6))\n",
    "ax2 = fig.add_subplot(111)\n",
    "ax2.set_xlabel('X', fontsize=14)\n",
    "ax2.set_ylabel('Y', fontsize=14)\n",
    "ax2.contourf(x, y, z, rstride=50, cstride=50, cmap='jet')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6fe1d644",
   "metadata": {},
   "source": [
    "边际密度函数：\n",
    "\n",
    "如果二维连续随机变量 $(X, Y)$ 的联合密度函数为 $p(x, y)$， 因为\n",
    "$$\n",
    "\\begin{aligned}\n",
    "&F_{X}(x)=F(x, \\infty)=\\int_{-\\infty}^{x}\\left(\\int_{-\\infty}^{\\infty} p(u, v) \\mathrm{d} v\\right) \\mathrm{d} u=\\int_{-\\infty}^{x} p_{X}(u) \\mathrm{d} u \\\\\n",
    "&F_{Y}(y)=F(\\infty, y)=\\int_{-\\infty}^{y}\\left(\\int_{-\\infty}^{\\infty} p(u, v) \\mathrm{d} u\\right) \\mathrm{d} v=\\int_{-\\infty}^{y} p_{Y}(v) \\mathrm{d} v\n",
    "\\end{aligned}\n",
    "$$\n",
    "其中 $p_{X}(x)$ 和 $p_{Y}(y)$ 分别为\n",
    "$$\n",
    "\\begin{aligned}\n",
    "&p_{X}(x)=\\int_{-\\infty}^{\\infty} p(x, y) \\mathrm{d} y \\\\\n",
    "&p_{Y}(y)=\\int_{-\\infty}^{\\infty} p(x, y) \\mathrm{d} x\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "【例子】设二维随机变量 $(X, Y)$ 的联合密度函数为\n",
    "$$\n",
    "p(x, y)= \\begin{cases}1, & 0<x<1,|y|<x, \\\\ 0, & \\text { 其他. }\\end{cases}\n",
    "$$\n",
    "试求: 边际密度函数 $p_{X}(x)$ 和 $p_{Y}(y)$。\n",
    "$$\n",
    "p_{x}(x)= \\begin{cases}2 x, & 0<x<1, \\\\ 0, & \\text { 其他. }\\end{cases}\n",
    "$$\n",
    "与\n",
    "$$\n",
    "p_{Y}(y)= \\begin{cases}1+y, & -1<y<0, \\\\ 1-y, & 0<y<1, \\\\ 0, & \\text { 其他. }\\end{cases}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "866efdb1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 求边际密度函数 p_{X}(x)\n",
    "from sympy import *\n",
    "x = symbols('x')\n",
    "y = symbols('y')\n",
    "p_xy = Piecewise((1,And(x>0,x<1,y<x,y>-x)),(0,True))\n",
    "integrate(p_xy, (y, -oo, oo))   ## 由于0<x<1时候，那么x>-x，即2x\n",
    "\n",
    "# 求边际密度函数 p_{Y}(y)\n",
    "from sympy import *\n",
    "x = symbols('x')\n",
    "y = symbols('y')\n",
    "p_xy = Piecewise((1,And(x>0,x<1,y<x,y>-x)),(0,True))\n",
    "integrate(p_xy, (x, -oo, oo))   ## 由于|y|<x,0<x<1时，因此y肯定在(-1,1)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.9.12 ('base')",
   "language": "python",
   "name": "python3912jvsc74a57bd096f00530df6dbe9a09a68470253b0890ebe3f8d769efa151705a0922e1443c12"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
